Erlangsformler

Erlangsformler, also known as Erlang formulas, are a set of mathematical equations used to calculate the blocking probability or the number of lines needed in a telecommunications system to achieve a certain grade of service. They were developed by Danish engineer Agner Krarup Erlang in the early 20th century.

The core of the Erlang formulas lies in modeling the arrival of calls or requests as a Poisson process and the duration of these calls as exponentially distributed. This leads to a system that can be analyzed using Markov chains. The most common formula, Erlang B, calculates the probability that all available lines or servers in a system are busy, resulting in a call being blocked.

The Erlang B formula requires three key inputs: the number of available lines (c), and the offered load (A), which is the average number of calls that would be in progress if there were an infinite number of lines. The formula is often presented as a recursive relation or a direct formula involving powers and factorials.

Erlang C is another important formula. Unlike Erlang B, it assumes that blocked calls are not lost but are instead queued. Erlang C calculates the probability that a call will have to wait in a queue, and also the average waiting time. This formula is crucial for designing systems with waiting lines, such as call centers.

Erlangsformler are fundamental tools in traffic engineering and capacity planning for various communication systems, including telephone networks, cellular networks, and call centers. They help determine the optimal number of resources needed to meet desired service levels while minimizing costs.